VANCOUVER, British Columbia, Sept 24 (Reuters) - Canada's banking regulator said on Monday it has received two applications from groups wanting to set up the first Islamic banks in the country, a small but growing industry in Western nations.

"In terms of formal applications, this would be the first two," said Normand Bergevin, managing director of approvals and precedents at the Office of the Superintendent of Financial Institutions (OSFI).

Islamic finance complies with the religion's ban on charging interest -- a key facet of traditional banking -- and on investing in products associated with alcohol and gambling.

The industry is estimated to be growing 15 percent a year, and large Western banks such as HSBC Holdings Plc (HSBA.L: Quote, Profile , Research) and Barclays Plc (BARC.L: Quote, Profile , Research) have set up Islamic banking arms.

Stuart Carruthers, a partner at law firm Stikeman Elliott in Toronto, said Canada was a potentially attractive market for Islamic banking services as it had a large and growing Muslim population. Families were often large, young and with a growing need for banking services.

Bergevin declined to identify the two applicants but said they were "not necessarily" from foreign banks.

He said the process to get approval to set up a bank was intricate and would take six months at the very least. In the case of a new area such as Islamic banking, it could take longer.

"When the business plan incorporates a lot of products that we are not familiar with, it might take us longer to review. To supervise the bank, we have to understand its products," he told Reuters in an interview.

After analyzing the application, OSFI would make a recommendation to the federal finance minister, who has the final say.